Skip to main content
SpringerLink
Log in

On computing Hilbert class fields of prime degree

  • Conference paper
  • First Online:
Algorithmic Number Theory (ANTS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1122))

Included in the following conference series:

  • 2609 Accesses

Abstract

In the sequel of our recent work on relative extensions of algebraic number fields [DaPo95] we extend the methods presented there for computing Hilbert class fields of degree three over totally real cubic fields. This is the first progress in arithmetic class field computations since Hasse's paper [Ha].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Cohen, A Course in Computational Algebraic Number Theory, 1. Aufl., Springer Verlag 1993.

    Google Scholar 

  2. M. Daberkow, Computations with relative extensions I, II, to appear.

    Google Scholar 

  3. M. Daberkow and M. Pohst, Computations with relative extensions of number fields with an application to the construction of Hilbert class fields, ISSAC'95 Proc.

    Google Scholar 

  4. M. Daberkow and M. Pohst, On the computation of Hilbert class fields, to appear.

    Google Scholar 

  5. H. Hasse, Über den Klassenkörper zum quadratischen Zahlkörper mit der Diskriminante-47, Acta Arith. 9, 419–434.

    Google Scholar 

  6. E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer Verlag 1981.

    Google Scholar 

  7. Kant group, KANT V4, submitted to Journal of Symbolic Computations.

    Google Scholar 

  8. S. Lang, Algebraic number theory, Graduate Texts in Mathematics 110, Springer Verlag 1986.

    Google Scholar 

  9. S. Lang, Cyclotomic fields I and II. Combined 2nd ed., Graduate Texts in Mathematics 121, Springer Verlag 1990.

    Google Scholar 

  10. J. Neukirch, Algebraische Zahlentheorie, 1. Aufl., Springer Verlag 1992.

    Google Scholar 

  11. P.L. Montgomery, Square roots of products of algebraic numbers, Proceedings of Symposia in Applied Mathematics, Vol. 48 (1994), 567–571.

    Google Scholar 

  12. M. Pohst, Computational algebraic number theory, DMV Seminar Bd. 21, Birkhäuser Verlag 1993.

    Google Scholar 

  13. M. Pohst, A. Schwarz and F. Diaz y Diaz, A Table of Quintic Fields, Math. Comp. 63 (1994), 361–376.

    Google Scholar 

  14. M. Pohst und H. Zassenhaus, Algorithmic algebraic number theory, Cambridge University Press 1989.

    Google Scholar 

  15. I.R. Shafarevich, A new proof of the Kronecker Weber theorem, Shafarevich, Collected Mathematical Papers, Springer Verlag 1989.

    Google Scholar 

  16. H.M. Stark, L-functions at s=1. IV. First derivatives as s=0., Adv. Math. 35, 197–235.

    Google Scholar 

  17. B. M. Trager, Algebraic Factoring and Rational Function Integration, Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, 219–226.

    Google Scholar 

  18. L. Washington, Introduction to cyclotomic fields. Graduate Texts in Mathematics 83, Springer Verlag 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Berlin, Fachbereich 3 Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany

    M. Daberkow & M. E. Pohst

Authors
  1. M. Daberkow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. E. Pohst
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Henri Cohen

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Daberkow, M., Pohst, M.E. (1996). On computing Hilbert class fields of prime degree. In: Cohen, H. (eds) Algorithmic Number Theory. ANTS 1996. Lecture Notes in Computer Science, vol 1122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61581-4_42

Download citation

  • DOI: https://doi.org/10.1007/3-540-61581-4_42

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61581-1

  • Online ISBN: 978-3-540-70632-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation